%\usepackage[brazil]{babel}
\usepackage[utf8]{inputenc}
%\usepackage{lmodern}
\usepackage{graphicx}
\usepackage{pifont}
%\usepackage{subfigure}
%\usepackage{psfrag}
%\usepackage{latexsym}
\usepackage{natbib}
\usepackage{color}
\usepackage{booktabs}
\usepackage{subfig}
%\usepackage{enumerate}
%\usepackage{pifont}
\usepackage{listings}
\usepackage{url}
\usepackage{amsmath}
\usepackage{soul}
\usepackage{amssymb} 
\usepackage[geometry]{ifsym} 
\definecolor{bgcode1}{cmyk}{0.17255,0.00000,0.28235,0.08627}
%\definecolor{bgcode}{rgb}{ 0.98823529,  0.98823529,  0.58039216}
\definecolor{bgmark}{gray}{0.9}
%\definecolor{bgcode}{gray}{0.9}
\definecolor{bgcode}{cmyk}{0.00000,0.23529,0.39216,0.26275}
\usepackage{balance}



%%%%%%%%%%symbols DEF USUARIO%%%%%
\newcommand{\Haut}{H=(X,\Sigma,f,\Gamma,x_0,X_m)}
\newcommand{\set}[1]{ \left \{ {#1}  \right \} }
\newcommand{\onesmall}{\text{\tiny 1}}
\newcommand{\zerosmall}{\text{\tiny 0}}
\newcommand{\twosmall}{\text{\tiny 2}}
\newcommand{\nsmall}{\text{\tiny n}}
\newcommand{\msmall}{\text{\tiny m}}
\newcommand{\Gaut}[1][]{{G}_{#1}=(X_{#1},\Sigma_{#1},\delta_{#1},\Gamma_{#1},x_{0{#1}},X_{m{#1}})}
\newcommand{\Buchi}[1][]{{\mathcal{B}}_{#1}=(X_{#1},\Sigma_{#1},f_{#1},\Gamma_{#1},x_{0{#1}},X_{m{#1}})}
\newcommand{\Gop}[1][]{{G_{op}}_{#1}=(X_{#1},\Sigma_{#1},f_{#1},\Gamma_{#1},x_{0_{#1}},X_{m_{#1}})}
\newcommand{\Gautnd}[1][]{{G}_{#1}=(X_{#1},\Sigma_{#1},\delta_{#1},\Gamma_{#1},X_{0_{#1}},X_{m_{#1}})}
\newcommand{\Hautnd}[1][]{{H}_{#1}=(X_{#1},\Sigma_{#1},f_{#1},\Gamma_{#1},X_{0{#1}},X_{m{#1}})}
\newcommand{\Gautdet}[1][]{{G}_{#1}=(X_{#1},\Sigma_{#1},f_{#1},\Gamma_{#1},x_{0,{#1}},X_{m,{#1}})}
\newcommand{\Gauteps}[1][]{{G_{\epsilon}}_{#1}=(X_{#1},\Sigma \cup \{\epsilon\} {#1},f_{u}{#1},\Gamma_{#1},X_{0_{#1}},X_{m_{#1}})}
\newcommand{\Galt}[1][]{{G'}_{#1}=(X_{#1},\Sigma_{#1},T,X_{0_{#1}},X_{m_{#1}})}
\newcommand{\Eset}{\Sigma}
\newcommand{\Eo}{\Sigma_o}
\newcommand{\Eisf}{\Sigma_{isf}}
\newcommand{\Esf}{\Sigma_{sf}}
\newcommand{\Eocp}{{\Sigma_o^c}'}
\newcommand{\Euo}{\Sigma_{uo}}
\newcommand{\Ef}{\Sigma_f}
\newcommand{\Efi}{\Sigma_{f_i}}
\newcommand{\Pif}{\Pi_f}
\newcommand{\sbar}{\overline{s}}
\newcommand{\Poinv}{P_{\Eo}^{-1}}%\newcommand{\Poinv}{P_{o_L}^{-1}}
\newcommand{\ef}{\sigma_f}
\newcommand{\ur}{\text{\it UR}}
\newcommand{\er}{\epsilon\!\text{\it R}}
\newcommand{\obs}{\text{\it Obs\,}}
\newcommand{\Xobs}{X_{\text{\it obs}}}
\newcommand{\fobs}{f_{\text{\it obs}}}
\newcommand{\xinobs}{x_{0_{\text{\it obs}}}}
\newcommand{\Xmobs}{X_{m_{\text{\it obs}}}}
\newcommand{\Gamobs}{\Gamma_{\text{\it obs}}}
\newcommand{\diag}{\text{\it Diag}}
\newcommand{\ev}{\sigma}
\newcommand{\Xd}{X_d}
\newcommand{\xd}{x_d}
\newcommand{\xdone}{x_{d_1}}
\newcommand{\xdi}{x_{d_i}}
\newcommand{\xdij}{x_{d_{ij}}}
\newcommand{\Xdi}{X_{d_i}}
\newcommand{\xdin}{x_{\zerosmall_d}}
\newcommand{\xdini}{x_{\zerosmall_{d_{i}}}}
\newcommand{\fd}{f_d}
\newcommand{\fdi}{f_{d_i}}
\newcommand{\Gamd}{\Gamma_d}
\newcommand{\Gamdi}{\Gamma_{d_i}}
\newcommand{\xzerod}{x_{{\zerosmall}_d}}
\newcommand{\xzero}{x_{\zerosmall}}
\newcommand{\Eoone}{\Sigma_{o_1}}
\newcommand{\Eotwo}{\Sigma_{o_2}}
\newcommand{\Eothree}{\Sigma_{o_3}}
\newcommand{\Eon}{\Sigma_{o_N}}
\newcommand{\Eoi}{\Sigma_{o_i}}
\newcommand{\Gdi}{G_{d_i}}
\newcommand{\Gd}{G_d}
\newcommand{\Gtestn}{G_{\text{test}_N}}
\newcommand{\Gtest}{G_{\text{test}}}
\newcommand{\Gtestthree}{G_{\text{test}_3}}
\newcommand{\Ht}{\tilde{H}}
\newcommand{\Xt}{\tilde{X}}
\newcommand{\xt}{\tilde{x}}
\newcommand{\yt}{\tilde{y}}
\newcommand{\ft}{\tilde{f}}
\newcommand{\Gamt}{\tilde{\Gamma}}
\newcommand{\xzerot}{\tilde{x}_{\zerosmall}}
\newcommand{\Hhat}{\hat{H}}
\newcommand{\xhat}{\hat{x}}
\newcommand{\Xhat}{\hat{X}}
\newcommand{\fhat}{\hat{f}}
\newcommand{\Gamhat}{\hat{\Gamma}}
\newcommand{\xzerohat}{\hat{x}_{\zerosmall}}
\newcommand{\oprime}{\text{o'}}
\newcommand{\uoprime}{\text{uo'}}
\newcommand{\isf}{\text{isf}}
\newcommand{\uo}{\text{uo}}
\newcommand{\Eess}{\Eset_{\text{ess}}}
\newcommand{\Ered}{\Eset_{\text{red}}}
\newcommand{\Edes}{\Eset_{\text{des}}}
\newcommand{\Eedes}{\Eset_{\text{edes}}}
\newcommand{\Eapes}{\Eset_{\text{apes}}}
\newcommand{\Eeapes}{\Eset_{\text{eapes}}}
\newcommand{\sinf}{s_{\infty}}
\newcommand{\Ld}{L_d}
\newcommand{\Iset}{{\cal I}}
\newcommand{\Rcal}{{\cal R}}
\newcommand{\Pcal}{{\cal P}}
\newcommand{\xdunc}[1][]{x_{d_{unc_{#1}}}}
\newcommand{\xdcert}[1][]{x_{d_{cert_{#1}}}}
\newcommand{\Xdcert}{X_{d_{cert}}}
\newcommand{\Xdunco}{X_{d_{unc_o}}}
\newcommand{\aut}[1]{\mathcal{#1}}
%\newcommand{\e}[1]{^{#1}}
\newcommand{\ksup}{K^{\uparrow C}}
%%%%Mathematical miscelaneous

\newcommand{\hs}[1]{\mathbb{H} \left \{ {#1}  \right \} }
\newcommand{\ps}[1]{ \left ( {#1}  \right ) }
\newcommand{\pcs}[1]{ \left [ {#1}  \right ] }
\newcommand{\ls}[1]{ \left \{ {#1}  \right \} }
\newcommand{\pang}[1]{ \left \langle  {#1} \right \rangle  }
\newcommand{\abs}[1]{ \left | {#1}  \right | }
\newcommand{\abseq}[1]{ \left \Vert {#1}  \right \Vert }
\newcommand{\re}{\mathbb{R}}
\renewcommand{\epsilon}{\varepsilon}
\newcommand{\blanc}{$\Box$}
\newcommand{\qedef}{\hfill \ding{113}}

%%%% command utilities


%\newcommand{\todo}[1]{\vspace*{3cm} \textcolor{red}{\emph{todo...{#1}}}}
\newcommand{\todo}[1]{\textcolor{blue}{ \emph{todo,...{#1}}} \vspace*{0.5cm}}
\newcommand{\nonrev}[1]{\textcolor{violet}{ \emph{nonrevised--{#1}}}}
\newcommand{\done}[1]{\textcolor{green}{ \emph{revised--{#1}}}}
\newcommand{\duvida}[1]{\textcolor{green}{\emph{duvida-{#1}}}}
\newcommand{\toref}[1]{\textcolor{red}{\emph{ref-{#1}}}}

\newlength{\sepgraf}
\newlength{\widetab}


%%%% theorem environments

%\newtheorem{algorithm}{Algoritmo}
%%\newtheorem{proposition}{Proposição}[chapter]
%%\newtheorem{remark}{Observação}[chapter]
%%\newtheorem{example}{Exemplo}
%%\newtheorem{definition}{Definição}[chapter]
%%\newtheorem{notation}{notação}[chapter]
%%\newtheorem{teorema}{Teorema}[chapter]
%%%\newtheorem{fact}{Fato}
%%%\newtheorem{procedure}{Procedimento}
%%\newtheorem{lema}{Lema}[chapter]
%%%\newtheorem{corolario}{Corolrio}[chapter]
%%%\newtheorem{proof}{Prova}
\newtheorem{ex1}{Example}

%% end of prove environment
\def\QED{\mbox{\rule[0pt]{1.5ex}{1.5ex}}}
%\def\proof{\noindent\hspace{2em}{\it Prova: }}
\def\proof{\noindent{\it \textbf{Prova: }}}
\def\endproof{\hspace*{\fill}~\QED\par\endtrivlist\unskip}

%%% listing environment
%\renewcommand\listingscaption{Lista}
%\renewcommand\listoflistingscaption{Lista of Códigos}
\renewcommand{\topfraction}{0.85}
\renewcommand{\textfraction}{0.1}
\newcommand{\deslab}{\textsc{deslab}}
\newcommand{\python}{\textsc{python}}
\newcommand{\networkx}{\textsc{networkx}} 
